Hyun Chul Jang | Mass rigidity for asymptotically locally hyperbolic manifolds with boundary скачать в хорошем качестве

Hyun Chul Jang | Mass rigidity for asymptotically locally hyperbolic manifolds with boundary

General Relativity Workshop 5/2/2022 Speaker: Hyun Chul Jang Title: Mass rigidity for asymptotically locally hyperbolic manifolds with boundary Abstract: Asymptotically locally hyperbolic (ALH) manifolds are a class of manifolds whose sectional curvature converges to −1 at infinity. If a given ALH manifold is asymptotic to a static reference manifold, the Wang-Chruściel-Herzlich mass integrals are well-defined, which is a geometric invariant that essentially measure the difference from the reference manifold. In this talk, I will present the result that an ALH manifold which minimize the mass integrals admits a static potential. To show this, we proved the scalar curvature map is locally surjective when it is defined on (1) the space of ALH metrics that coincide exponentially toward the boundary or (2) the space of ALH metrics with arbitrarily prescribed nearby Bartnik boundary data. And then, we establish the rigidity of the known positive mass theorems by studying the static uniqueness. This talk is based on joint work with L.-H. Huang.